Value sets of bivariate folding polynomials over finite fields

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2018-11-01

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Küçüksakallı, Ömer

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We find the cardinality of the value sets of polynomial maps associated with simple complex Lie algebras B-2 and G(2) over finite fields. We achieve this by using a characterization of their fixed points in terms of sums of roots of unity.

Subject Keywords

Lie algebra, Weyl group, Fixed point, Permutation

URI

https://hdl.handle.net/11511/32985

Journal

FINITE FIELDS AND THEIR APPLICATIONS

DOI

https://doi.org/10.1016/j.ffa.2018.05.008

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Department of Mathematics, Article

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Value sets of folding polynomials over finite fields Küçüksakallı, Ömer (2019-01-01) Let k be a positive integer that is relatively prime to the order of the Weyl group of a semisimple complex Lie algebra g. We find the cardinality of the value sets of the folding polynomials P-g(k)(x) is an element of Z[x] of arbitrary rank n >= 1, over finite fields. We achieve this by using a characterization of their fixed points in terms of exponential sums.
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Value sets of bivariate Chebyshev maps over finite fields Küçüksakallı, Ömer (2015-11-01) We determine the cardinality of the value sets of bivariate Chebyshev maps over finite fields. We achieve this using the dynamical properties of these maps and the algebraic expressions of their fixed points in terms of roots of unity.
Exceptional Lie algebra g2 and its representations Kayakökü, Mehmet Mustafa; Ünal, İbrahim; Department of Mathematics (2022-9-01) In the classification of complex simple Lie algebras, there are five of them whose Dynkin diagrams are of exceptional type. The Lie algebra g_2 has the smallest dimension among these exceptional Lie algebras and together with its corresponding Lie group G_2, it plays an important role in differential geometry, mathematical physics, and modern string theory. In this thesis after a general introduction to Lie algebras, we show the classification of complex simple ones. Afterward, we give several constructions...

Citation Formats

Ö. Küçüksakallı, “Value sets of bivariate folding polynomials over finite fields,” FINITE FIELDS AND THEIR APPLICATIONS, pp. 253–272, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/32985.